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It is shown that for arbitrary connection in the vector bundle compatible with some Hermitian metric, the corresponding Fedosov trace functional commutes with involution generated by this metric.
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Chamseddine, A.H.: SL(2,C) gravity with a complex vierbein and its noncommutative extension, Phys. Rev. D 69, 024015 (2004), hep-th/0309166
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Mukherjee, P. and Saha, A.: Note on the noncommutative correction to gravity, Phys. Rev. D 74
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Dobrski, M.: Some models of geometric noncommutative general relativity, Phys. Rev. D 84
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Bieliavsky, P., Cahen, M., Gutt, S., Rawnsley, J. and Schwachhöfer, L.: Symplectic connections, Int. J. Geom. Meth. Mod. Phys. 3
2006
Cited alongside, same era.